Vítězslav Kala, Tomáš Kepka, Miroslav Korbelář
Notes on commutative parasemifields

Comment.Math.Univ.Carolin. 50,4 (2009) 521-533.

Abstract:Parasemifields (i.e., commutative semirings whose multiplicative semigroups are groups) are considered in more detail. We show that if a parasemifield $S$ contains $\Bbb Q^+$ as a subparasemifield and is generated by $\Bbb Q^{+}\cup \{a\}$, $a\in S$, as a semiring, then $S$ is (as a semiring) not finitely generated.

Keywords: semiring, ideal-simple, parasemifield, finitely generated
AMS Subject Classification: 16Y60